Institut für Mathematik


Prof. Dr. Jean Bertoin

Institut für Mathematik
Institut für Mathematik, Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

Fax: +41 44 635 57 06
Büro: Y27J36
Franziska Robmann

+41 44 635 58 31

Lecture & Seminar

Research seminars
Seminar über stochastische Prozesse
Jean Bertoin, Erwin Bolthausen, Alain-Sol Sznitman, Vincent Tassion



University of Zürich - open access archive


hal - preprints


J. Bertoin
Random Fragmentation and Coagulation Processes
Cambridge Studies in Advanced Mathematics 102   
Cambridge University Press, 2006

J. Bertoin
Lévy Processes
Cambridge Tracts in Mathematics 121   
Cambridge University Press, 1996 (2nd edition 1998)

Publications since 1999

for a complete list please contact Prof. Dr. Jean Bertoin

J. Bertoin
Reinforced Galton-Watson processes II: Large time behaviors

J. Bertoin, B. Mallein
Reinforced Galton-Watson processes I: Malthusian exponents
Random Structures & Algorithms, first published: 22 April 2024   

J. Bertoin
A model for an epidemic with contact tracing and cluster isolation, and a detection paradox
J. Appl. Probab. 60 (2023), no. 3, 1079–1095.

J. Bertoin
Limits of Pólya urns with innovations
Electron. J. Probab. 28: 1-19 (2023)

J. Bertoin
On the local times of noise reinforced Bessel processes
Annales Henri Lebesgue, Volume 5 (2022), pp. 1277-1294.

J. Bertoin
Counting the zeros of an elephant random walk
Trans. Amer. Math. Soc. 375 (2022), 5539-5560.
Article electronically published on March 31, 2022   

J. Bertoin, H. Yang
Scaling limits of branching random walks and branching stable processes
J. Appl. Probab. 59.4, 2022

J. Bertoin
Counterbalancing steps at random in a random walk
J. Eur. Math. Soc. (JEMS), 1 - 23, 2023, online first

E. Baur, J. Bertoin
On a two-parameter Yule-Simon distribution
In: Chaumont, L., Kyprianou, A.E. (eds) A Lifetime of Excursions Through Random Walks and Lévy Processes. Progress in Probability, vol 78. Birkhäuser, Cham, 2022

J. Bertoin, N. Curien, I. Kortchemski
On conditioning a self-similar growth-fragmentation by its intrinsic area
Ann. Inst. H. Poincaré Probab. Statist. 57(2), 1136 - 1156, 2021

J. Bertoin
Scaling exponents of step-reinforced random walks
Probab. Theory Relat. Fields, 179, 295–315, 2021

J. Bertoin
Universality of Noise Reinforced Brownian Motions
In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, 2021

J. Bertoin
How linear reinforcement affects Donsker's theorem for empirical processes
Probab. Theory Relat. Fields, 2020

J. Bertoin
Noise reinforcement for Lévy processes
Annales de l’Institut Henri Poincaré, Probab. Statist., vol 56-3, 2236 - 2252, 2020

J. Bertoin, A. Watson
The strong Malthusian behavior of growth-fragmentation processes
Annales Henri Lebesgue, 3, 795 - 823, 2020

J. Bertoin
A version of Herbert A. Simon's model with slowly fading memory and its connections to branching processes
Journal of Statistical Physics, pp 1–13, 2019

J. Bertoin
On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors
Journal of Functional Analysis, available online June 2019

J. Bertoin, B. Mallein
Infinitely ramified point measures and branching Lévy processes
Ann. Probab., 47 - 3, 1619 - 1652, 2019

J. Bertoin
Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Lévy processes
Stochastic Processes and their Applications, vol. 129-4, 1443-1454, 2019

J. Bertoin, A. Cortines Peixoto, B. Mallein
Branching-stable point measures and processes
Advances in Applied Probability, vol. 50-4, 1294-1314, 2018

J. Bertoin, B. Mallein
Biggins' Martingale Convergence for Branching Lévy Processes
Electron. Commun. Probab. 23, paper no. 83, 2018

J. Bertoin, N. Curien, I. Kortchemski
Random planar maps & growth-fragmentations
Annals of Probability, vol. 46-1, 207-260, 2018

J. Bertoin, A. Watson
A probabilistic approach to spectral analysis of growth-fragmentation equations
Journal of Functional Analysis, 274, 8, 2163-2204, 2018

J. Bertoin, T. Budd, N. Curien, I. Kortchemski
Martingales in self-similar growth-fragmentations and their connections with random planar maps
Probability Theory and Related Fields, 1-62, 2017

E. Baur, J. Bertoin
Weak limits for the largest subpopulations in Yule processes with high mutation probabilities
Advances in Applied Probability 49-3, 877-902, 2017

J. Bertoin
Markovian growth-fragmentation processes
Bernoulli 23, 1082-1101, 2017

E. Baur, J. Bertoin
Sur la destruction de grands arbres aléatoires récursifs
Gazette des mathématiciens, vol. 150, 41-47, 2016

E. Baur, J. Bertoin
Elephant Random Walks and their connection to Pólya-type urns
Phys. Rev. E, vol. 94-5, 052134, 2016

J. Bertoin
Mathematical Models for Population Dynamics: Randomness versus Determinism
Mathematics and Society, EMS Publishing House, 81 - 99, 2016

J. Bertoin, R. Stephenson
Local explosion in self-similar growth-fragmentation processes
Electron. Commun. Probab. , vol. 21, 21 - 66, 2016

J. Bertoin, A. Watson
Probabilistic aspects of critical growth-fragmentation equations
Advances in Applied Probability, vol. 48, Issue A, 37 - 61, July 2016

J. Bertoin, I. Kortchemski
Self-similar scaling limits of Markov chains on the positive integers
Ann. Appl. Probab 26, 2556-2595, 2016

J. Bertoin
Marc Yor et les temps locaux
Marc Yor - La passion du mouvement brownien

Numéro spécial Gazette des Mathématiciens - Matapli, 25-38, 2015

E. Baur, J. Bertoin
The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes
Electron. J. Probab. 20, no. 98, 1-20, 2015

J. Bertoin
The cut-tree of large recursive trees
Annales de l’Institut Henri Poincaré 51, 478 - 488, 2015

J. Bertoin
Compensated fragmentation processes and limits of dilated fragmentations
Ann. Probab. 44, 1254-1284, 2016

J. Bertoin, G. Uribe Bravo
Supercritical percolation on large scale-free random trees
Annals of Applied Probability, vol. 25-1, 81 - 130, 2015

E. Baur, J. Bertoin
Cutting edges at random in large recursive trees
Stochastic Analysis and Applications, Springer, 51 - 76, 2014

J. Bertoin, M. Yor
Local times for functions with finite variation: two versions of Stieltjes change of variables formula
Bull. London Math. Soc. 46, 553 - 560, 2014

J. Bertoin
On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees
Electron. J. Probab. 19, No 24, 2014

J. Bertoin
Hoy día, ¿podemos confiar en la estadística?
Cró, Nov. 2013

J. Bertoin, M. Yor
Pure jump increasing processes and the change of variables formula
Electron. Commun. Probab. 18, No. 4, 2013

J. Bertoin
Paul Lévy et l'arithmétique des lois de probabilités
ESAIM Probability and Statistics 17, 790 - 794, 2013

J. Bertoin
Almost giant clusters for percolation on large trees with logarithmic heights
J. Appl. Prob. 50, 603 - 611, 2013

J. Bertoin
On largest offsprings in a critical branching process with finite variance
J. Appl. Prob. 50, 791 - 800, 2013

J. Bertoin, G. Miermont
The cut-tree of large Galton-Watson trees and the Brownian CRT
Ann. Appl. Probab. 23, 1469 - 1493, 2013

J. Bertoin, D. Dufresne, M. Yor
Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion
Rev. Mat. Iberoam. 29, 4, 1307 - 1324, 2013

J. Bertoin
Sizes of the largest clusters for supercritical percolation on random recursive trees
Random Struct. Alg. 44, 29 – 44, 2014

J. Bertoin, M. Yor
Retrieving information from subordination
Prokhorov and Contemporary Probability Theory
Eds: Albert N. Shiryaev, S. R. S. Varadhan, Ernst L. Presman   
Springer, 97 - 106, 2013.

J. Bertoin
Coagulation with limited aggregations
European Congress of Mathematics, EMS, 195 - 209, 2012

J. Bertoin
The area of a self-similar fragmentation
Alea, Volume IX, 53 - 66, 2012

J. Bertoin
Fires on trees
Annales de l'Institut Henri Poincaré Probabilités et Statistiques 48(4), 909 - 921, 2012

J. Bertoin, M. Barczy
Functional limit theorems for Lévy processes satisfying Cramér's condition
Electronic J. of Probability 16, 2020 - 2038, 2011   

J. Bertoin
On the maximal offspring in a critical branching process with infinite mean
J. Appl. Probab. 48, 576 - 582, 2011   

J. Bertoin
Burning cars in a parking lot
Commun. Math. Phys. 306, 261 - 290, 2011   

J. Bertoin
Some applications of duality for Lévy processes in a half-line
Bull. London Math. Soc. 43, 97 - 110, 2011   

J. Bertoin, J. Berestycki, B. Haas, G. Miermont
Quelques aspects fractals des processus de fragmentation aléatoire
Quelques interactions entre analyse, probabilités et fractals
Panorama et Synthèses 32, 191 - 243, 2010   

J. Bertoin
Asymptotic regimes for the partition into colonies of a branching process with emigration
Ann. Appl. Probab. 20, 1967 - 1988, 2010   

J. Bertoin
A two-time-scale phenomenon for a fragmentation-coagulation process
Electron. Commun. Probab. 15, 253 - 262, 2010   

J. Bertoin
A limit theorem for trees of alleles in branching processes with rare neutral mutations
A tribute to Kiyosi Itô

Stochastic Process. Appl. 120, 678 - 697, 2010   

J. Bertoin, V. Sidoravicius, M.E. Vares
A system of grabbing particles related to Galton-Watson trees
Random Structures Algorithms 36, 477 - 487, 2010   

J. Bertoin
Two solvable systems of coagulation equations with limited aggregations
Ann. Inst. Henri Poincaré 26, 2073 - 2089, 2009   

J. Bertoin
The structure of the allelic partition of the total population
for Galton-Watson processes with neutral mutations

Ann. Probab. 37, 1502 - 1523, 2009   

J. Bertoin, V. Sidoravicius
The structure of typical clusters in large sparse random configurations
J. Stat. Phys. 235, 87 - 105, 2009   

J. Bertoin, J. Fontbona, S. Martinez
On prolific individuals in a supercritical continuous state branching process
J. Appl. Probab. 45, 714 - 726   

J. Bertoin
Asymptotic regimes for the occupancy scheme of multiplicative escades
Stochastic Process. Appl. 118, 1586 - 1605, 2008   

J. Bertoin
Multitype homogeneous fragmentations
In and Out of Equilibrium 2
Eds. V. Sidoravicius and M.E. Vares
Progress in Probability, 161 - 183, 2008   

J. Bertoin
A second order SDE for the Langevin process reflected at a completely inelastic boundary
J. Euro. Math. Soc 10, 625 - 639, 2008   

J. Bertoin, A. Lindner, R. Maller
On continuity properties of the law of integrals of Lévy processes
Séminaire de Probabilités XLI
Lecture Notes in Mathematics 1934, 137 - 159, Springer 2008   

J. Bertoin
Two-parameter Poisson-Dirichlet measures and reversible
exchangeable fragmentation-coalescence processes

Combin. Probab. Comp. 17, 329 - 337, 2008   

J. Bertoin, R. Doney, R. Maller
Passage of Lévy processes across power law boundaries at small times
Ann. Probab. 36, 160 - 197, 2008   

J. Bertoin
Reflecting a Langevin process at an absorbing boundary
Ann. Probab. 35, 2021 - 2037, 2007   

J. Bertoin, T. Fujita, B. Roynette, M. Yor
On a particular class of self-decomposable random variables: the duration
of a Bessel excursion straddling independent exponential times

Probab. Math. Stat 26, 315 - 366, 2006   

J. Bertoin, J.-F. Le Gall
Stochastic flows associated to coalescent processes III: Limits theorems
Illinois J. Math. 50, 147 - 181, 2006   

J. Bertoin, G. Miermont
Asymptotics in Knuth's parking problem for caravans
Random Structures Algorithms 29, 38 - 55, 2006   

J. Bertoin
Some aspects of a random fragmentation model
Stochastic Process. Appl. 116, 345 - 369, 2006   

J. Bertoin, M. Yor
Exponential functionals of Lévy processes
Probability Survey 2, 191 - 212, 2005   

J. Bertoin
SLE et invariance conforme (d'après Lawler, Schramm et Werner)
Séminaire Bourbaki, Volume 2003/2004
Astérisque 299, 15 - 28, 2005   

J. Bertoin, J.-F. Le Gall
Stochastic flows associated to coalescent processes II:
Stochastic differential equation

Ann. Inst. Henri Poincaré 41, 307 - 333, 2005   

J. Bertoin, S. Martinez
Fragmentation energy
Adv. Appl. Probab. 37, 553 - 570, 2005   

J. Bertoin, A. Rouault
Discretization methods for homogeneous fragmentations
J. London Math. Soc. 72, 91 - 109, 2005   

J. Bertoin, Ph. Biane, M. Yor
Poissonian exponential functionals, q-series, q-integrals,
and the moment problem for log-normal distributions

Seminar on Stochastic Analysis, Random Fields and Applications IV
Eds. R. Dalang, M. Dozzi, F. Russo
Progress in Probability 58, 45 - 56, Birkhäuser, 2004   

J. Bertoin, C. Goldschmidt
Dual random fragmentation and coagulation and an application
to the genealogy of Yule processes

Mathematics and Computer Science III: Algorithms, Trees,Combinatorics and Probabilities
Eds. M. Drmota, P. Flajolet, D. Gardy, B. Gitttenberger
295 - 308, Birkhäuser, 2004   

J. Bertoin, A. V. Gnedin
Asymptotic laws for nonconservative self-similar fragmentations
Electron. J. Probab. 9, 575 - 593, 2004   

J. Bertoin
Random covering of an interval and a variation of Kingman's coalescent
Random Structures Algorithms 25, 277 -292, 2004   

J. Bertoin
Some aspects of random fragmentations in continuous times
Dynamics and Randomness II
Eds. A. Maass, S. Martinez, S. San Martin
Kluwer, 1 - 15, 2004   

J. Bertoin
On small masses in self-similar fragmentations
Stochastic Process. Appl. 109, 13 - 22, 2004   

J. Bertoin, L. Chaumont, J. Pitman
Path transformations of first passage bridges
Electron. Commun. Probab. 8, 155 - 166, 2003   

J. Bertoin
The asymptotic behavior of fragmentation processes
J. Euro. Math. Soc 5, 395 - 416, 2003   

J. Bertoin, J.-F. Le Gall
Stochastic flows associated to coalescent processes
Probab. Theory Relat. Fields 126, 261 - 288, 2003   

J. Bertoin, M. Yor
On the entire moments of self-similar Markov processes and exponential functionals
of certain Lévy processes

Ann. Fac. Sci. Toulouse Série 6, vol. XI, 33 - 45, 2002   

J. Bertoin
Self-attracting Poisson clouds in an expanding universe
Commun. Math. Phys. 232, 59 - 81, 2002   

J. Bertoin
Some aspects of additive coalescents
Proceedings ICM 2002 vol. III, Higher Education Press, 15 - 23, 2002   

J. Bertoin
Eternal solutions to Smoluchowski's coagulation equation with additive kernel
and their probabilistic interpretations

Ann. Appl. Probab. 12, 547 - 564, 2002   

J. Bertoin, M. Yor
Entrance laws of self-similar Markov processes and
exponential functionals of Lévy processes

Potential Analysis 17, 389 - 400, 2002   

J. Bertoin, M.-E. Caballero
Entrance from 0+ for increasing semi-stable Markov processes
Bernoulli 8, 195 - 205, 2002   

J. Bertoin
Self-similar fragmentations
Ann. Inst. Henri Poincaré 38, 319 - 340, 2002   

J. Bertoin, M. Yor
On subordinators, self-similar Markov processes, and some factorizations
of the exponential law

Electron. Commun. in Probab. 6, 95 - 106, 2001   

J. Bertoin, C. Giraud, Y. Isozaki
Statistics of a flux in Burgers turbulence with one-sided Brownian initial data
Commun. Math. Phys. 224, 551 - 564, 2001   

J. Bertoin
Homogeneous fragmentation processes
Probab. Theory Relat. Fields 121, 301 -318, 2001   

J. Bertoin
Eternal additive coalescents and certain bridges with exchangeable increments
Ann. Probab. 29, 344 - 360, 2001   

J. Bertoin
Some properties of Burgers turbulence with white or stable noise initial data
Eds. Barndorff-Nielson, Mikosch and Resnick
Lévy processes: theory and aplications, Birkhäuser, 267 - 279, 2001   

J. Bertoin
Elements on Lévy processes
Stochastic Processes: Theory and Methods
Handbook of Statistics 19, Elsevier, 117 - 144, 2001   

J. Bertoin
A fragmentation process connected to Brownian motion
Probab. Theory Relat. Fields 117, 289 - 301, 2000   

J. Bertoin, J.-F. Le Gall
The Bolthausen-Sznitman coalescent and the genealogy of
continuous-state branching processes

Probab. Theory Relat. Fields 117, 249 - 266, 2000   

J. Bertoin, J. Pitman
Two coalescents derived from the range of stable subordinators
Electron. J. Probab. 5, 1 - 17, 2000   

J. Bertoin
The convex minorant of the Cauchy process
Electron. Commun. in Probab. 5, 51 - 55, 2000   

J. Bertoin
Clustering statistics for sticky particles with Brownian initial velocity
J. Math. Pures Appl. 79, 173 - 194, 2000   

J. Bertoin
renewal theory for embedded regenerative sets
Ann. Probab. 27, 1523 - 1535, 1999   

J. Bertoin
Subordinators: Examples and Applications
Ecole d'été de Probabilités de St-Flour XXVII
Lect. Notes in Maths 1717, Springer, 1 - 91, 1999   

J. Bertoin, K. van Harn, F.W. Steutel
Renewal theory and level passage by subordinators
Stat. Probab. Letters 45, 65 - 69, 1999   

J. Bertoin
On overshoots and hitting times for random walks
J. Appl. Probab. 36, 593 - 600, 1999   

J. Bertoin, J. Pitman, J. Ruiz de Chavez
Construction of a Brownian path with a given minimum
Electron. Commun. in Probab. 4, 31 - 37, 1999   

J. Bertoin
Structure of shocks in Burgers turbulence with stable noise initial data
Commun. Math. Phys. 203, 729 - 741, 1999   

J. Bertoin
Intersection of independent regenerative sets
Probab. Theory Relat. Fields 114, 97 - 121, 1999   

J. Bertoin, M.-E. Caballero
Regularity of the Cauchy principal value of the local times of some Lévy processes
Bull. Sc. math. 123, 47 - 58, 1999   


Prof. Dr. Géronimo Uribe Bravo, Instituto de Matématicas, Universidad Nacional Autonoma de México (Ciudad de México, D.F., México)
Talk: A pathwise approach to time change
15.05.24 - 17.05.24Bertoin, Jean
Dr. Jean-Jil Duchamps, Laboratoire de Mathématiques de Besançon, Université de Franche-Comté (Besançon)
Talk: Local weak convergence for a general stochastic SIR model
20.03.24 - 21.03.24Bertoin, Jean
Dr. Victor Rivero, CIMAT (Guanajuato, Mexico)
Talk: Recurrent extensions and Stochastic Differential equations
11.03.24 - 15.03.24Bertoin, Jean